Invariant theory and reversible-equivariant vector fields

In this paper we present results for the systematic study of reversible-equivariant vector fields - namely, in the simultaneous presence of symmetries and reversing symmetries - by employing algebraic techniques from invariant theory for compact Lie groups. The Hilbert-Poincare series and their associated Molien formulae are introduced,and we prove the character formulae for the computation of dimensions of spaces of homogeneous anti-invariant polynomial functions and reversible-equivariant polynomial mappings. A symbolic algorithm is obtained for the computation of generators for the module of reversible-equivariant polynomial mappings over the ring of invariant polynomials. We show that this computation can be obtained directly from a well-known situation, namely from the generators of the ring of invariants and the module of the equivariants. (C) 2008 Elsevier B.V, All rights reserved.

A Parallel Hardware Architecture for Scale and Rotation Invariant Feature Detection

This paper proposes a parallel hardware architecture for image feature detection based on the Scale Invariant Feature Transform algorithm and applied to the Simultaneous Localization And Mapping problem. The work also proposes specific hardware optimizations considered fundamental to embed such a robotic control system on-a-chip. The proposed architecture is completely stand-alone; it reads the input data directly from a CMOS image sensor and provides the results via a field-programmable gate array coupled to an embedded processor. The results may either be used directly in an on-chip application or accessed through an Ethernet connection. The system is able to detect features up to 30 frames per second (320 x 240 pixels) and has accuracy similar to a PC-based implementation. The achieved system performance is at least one order of magnitude better than a PC-based solution, a result achieved by investigating the impact of several hardware-orientated optimizations oil performance, area and accuracy.

QCD sum rule calculation for the charmonium-like structures in the J/psi phi and J/psi omega invariant mass spectra

Using the QCD sum rules we test if the charmonium-like structure Y(4274), observed in the J/psi phi invariant mass spectrum, can be described with a D(s)(D) over bar (s0)(2317)+ h.c. molecular current with J(PC) = 0(-+). We consider the contributions of condensates up to dimension ten and we work at leading order in alpha(s). We keep terms which are linear in the strange quark mass m(s). The mass obtained for such state is mD(s)D(s0) = (4.78 +/- 0.54) GeV. We also consider a molecular 0(-+) D (D) over bar (0)(2400)+ h.c. current and we obtain m(DD0) = (4.55 +/- 0.49) GeV. Our study shows that the newly observed Y(4274) in the J/psi phi invariant mass spectrum can be, considering the uncertainties, described using a molecular charmonium current. (C) 2011 Elsevier B.V. All rights reserved.

A new scale-invariant ratio and finite-size scaling for the stochastic susceptible-infected-recovered model

The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered individuals is determined as a function of the infection rate for several values of the system size. The analysis around criticality is obtained by exploring the close relationship between the present model and standard percolation theory. The quantity UP, equal to the ratio U between the second moment and the squared first moment of the size distribution multiplied by the order parameter P, is shown to have, for a square system, a universal value 1.0167(1) that is the same for site and bond percolation, confirming further that the SIR model is also in the percolation class.

A conformal invariant growth model

We present a one-parameter extension of the raise and peel one-dimensional growth model. The model is defined in the configuration space of Dyck (RSOS) paths. Tiles from a rarefied gas hit the interface and change its shape. The adsorption rates are local but the desorption rates are non-local; they depend not only on the cluster hit by the tile but also on the total number of peaks (local maxima) belonging to all the clusters of the configuration. The domain of the parameter is determined by the condition that the rates are non-negative. In the finite-size scaling limit, the model is conformal invariant in the whole open domain. The parameter appears in the sound velocity only. At the boundary of the domain, the stationary state is an adsorbing state and conformal invariance is lost. The model allows us to check the universality of non-local observables in the raise and peel model. An example is given.

Quantized fields and gravitational particle creation in f (R) expanding universes

The problem of cosmological particle creation for a spatially flat, homogeneous and isotropic universes is discussed in the context of f (R) theories of gravity. Different from cosmological models based on general relativity theory, it is found that a conformal invariant metric does not forbid the creation of massless particles during the early stages (radiation era) of the universe. (C) 2010 Elsevier B.V. All rights reserved.

The Immunomodulatory Action of Sialostatin L on Dendritic Cells Reveals Its Potential to Interfere with Autoimmunity

Sialostatin L (SialoL) is a secreted cysteine protease inhibitor identified in the salivary glands of the Lyme disease vector Ixodes scapularis. In this study, we reveal the mechanisms of SialoL immunomodulatory actions on the vertebrate host. LPS-induced maturation of dendritic cells from C57BL/6 mice was significantly reduced in the presence of SialoL. Although OVA degradation was not affected by the presence of SialoL in dendritic cell cultures, cathepsin S activity was partially inhibited, leading to an accumulation of a 10-kDa invariant chain intermediate in these cells. As a consequence, in vitro Ag-specific CD4(+) T cell proliferation was inhibited in a time-dependent manner by SialoL, and further studies engaging cathepsin S(-/-) or cathepsin L(-/-) dendritic cells confirmed that the immunomodulatory actions of SialoL are mediated by inhibition of cathepsin S. Moreover, mice treated with SialoL displayed decreased early T cell expansion and recall response upon antigenic stimulation. Finally, SialoL administration during the immunization phase of experimental autoimmune encephalomyelitis in mice significantly prevented disease symptoms, which was associated with impaired IFN-gamma and IL-17 production and specific T cell proliferation. These results illuminate the dual mechanism by which a human disease vector protein modulates vertebrate host immunity and reveals its potential in prevention of an autoimmune disease. The Journal of Immunology, 2009, 182: 7422-7429.

Finite-dimensional global attractors in Banach spaces

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional. (C) 2010 Elsevier Inc. All rights reserved.

Distinguishing links up to link-homotopy by algebraic methods

In this paper we provide a complete algebraic invariant of link-homotopy, that is, an algebraic invariant that distinguishes two links if and only if they are link-homotopic. The paper establishes a connection between the ""peripheral structures"" approach to link-homotopy taken by Milnor, Levine and others, and the string link action approach taken by Habegger and Lin. (C) 2009 Elsevier B.V. All rights reserved.

SINGULARITY THEORY AND FORCED SYMMETRY BREAKING IN EQUATIONS

A theory of bifurcation equivalence for forced symmetry breaking bifurcation problems is developed. We classify (O(2), 1) problems of corank 2 of low codimension and discuss examples of bifurcation problems leading to such symmetry breaking.

DAMPED WAVE EQUATIONS WITH FAST GROWING DISSIPATIVE NONLINEARITIES

Let a > 0, Omega subset of R(N) be a bounded smooth domain and - A denotes the Laplace operator with Dirichlet boundary condition in L(2)(Omega). We study the damped wave problem {u(tt) + au(t) + Au - f(u), t > 0, u(0) = u(0) is an element of H(0)(1)(Omega), u(t)(0) = v(0) is an element of L(2)(Omega), where f : R -> R is a continuously differentiable function satisfying the growth condition vertical bar f(s) - f (t)vertical bar <= C vertical bar s - t vertical bar(1 + vertical bar s vertical bar(rho-1) + vertical bar t vertical bar(rho-1)), 1 < rho < (N - 2)/(N + 2), (N >= 3), and the dissipativeness condition limsup(vertical bar s vertical bar ->infinity) s/f(s) < lambda(1) with lambda(1) being the first eigenvalue of A. We construct the global weak solutions of this problem as the limits as eta -> 0(+) of the solutions of wave equations involving the strong damping term 2 eta A(1/2)u with eta > 0. We define a subclass LS subset of C ([0, infinity), L(2)(Omega) x H(-1)(Omega)) boolean AND L(infinity)([0, infinity), H(0)(1)(Omega) x L(2)(Omega)) of the `limit` solutions such that through each initial condition from H(0)(1)(Omega) x L(2)(Omega) passes at least one solution of the class LS. We show that the class LS has bounded dissipativeness property in H(0)(1)(Omega) x L(2)(Omega) and we construct a closed bounded invariant subset A of H(0)(1)(Omega) x L(2)(Omega), which is weakly compact in H(0)(1)(Omega) x L(2)(Omega) and compact in H({I})(s)(Omega) x H(s-1)(Omega), s is an element of [0, 1). Furthermore A attracts bounded subsets of H(0)(1)(Omega) x L(2)(Omega) in H({I})(s)(Omega) x H(s-1)(Omega), for each s is an element of [0, 1). For N = 3, 4, 5 we also prove a local uniqueness result for the case of smooth initial data.

Isometric immersions into a homogeneous Lorentzian Heisenberg group and rigidity

In this paper we prove an existence result for local and global isometric immersions of semi-Riemannian surfaces into the three dimensional Heisenberg group endowed with a homogeneous left-invariant Lorentzian metric. As a corollary, we prove a rigidity result for such immersions.

Stability of gradient semigroups under perturbations

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).